5 Answers
5

Although worth is sometimes a noun, in your examples it's an adjective. However, it's what the Cambridge Grammar of the English Language (CGEL) calls a "highly exceptional adjective" (p.607). Unlike most, it licenses NP complements, similar to a preposition:

It is worth [ it ]
It is worth [ 100 dollars ]
It is worth [ looking at ]
It is worth [ taking into consideration ]

CGEL presents arguments on pages 607-608 that worth is an adjective despite its differences from the rest of the category:

It occurs as complement to become:

i. What might have been a $200 first edition suddenly became [ worth perhaps 10 times that amount ] .

When functioning as an adjunct, it must have a predicand:

ii. [ Worth over a million dollars, ] the jewels were kept under surveillance by a veritable army of security guards.
iii. *[ Worth over a million dollars, ] there'll be ample opportunity for a lavish lifestyle.

They write "In [ii] the predicand of the worth AdjP is the subject the jewels, whereas in [iii] there is no such predicand and the result is inadmissable."

Worth cannot be pied-piped like a preposition:

This was far less than the amount [ which she thought the land was now worth ] .
*This was far less than the amount [ worth which she thought the land was now ] .

So although it's not like a regular adjective, it's also unlike a preposition; they choose to place it in the adjective category. However, it's also unlike the central members of that category:

It's not really gradable:

It's worth the effort.
*It's very worth the effort.

It doesn't really appear attributively, although this might be an expected consequence of requiring a complement (cf. *an afraid of bears man):

It was worth the effort.
*It was a worth the effort task.

And of course, it takes an NP complement, unlike other adjectives:

It was worth the effort.
*It was valuable the effort.

Of course, the point of placing words in categories in the first place is to reduce the amount of descriptive work you have to do. Place words that work the same way in the same category, and you can describe most of those words the same way. When you come across a word like worth which doesn't fit neatly into any category, you can pick any category it's close to and describe its differences from that category. You could, for example, describe it as an exceptional preposition.

What's most important, then, is not which category you place it into, but rather that you know specifically how it works. So to that end, saying worth is an adjective is only a starting point. After we say so, we must describe the ways it differs from its fellow adjectives.

Whereas value is a noun (with derived verbal senses), ... the categorial status of worth is a matter of some dispute. It has variously been claimed to be a preposition and an adjective (cf. Maling 1983 and McCawley 1985). If it is a preposition, then it must have a homophonous derived noun, since phrases like the worth of the book are common enough.

On the other hand, if it is an adjective, then it must be transitive, since it has a complement; this is surely unusual -- or even impossible, acording to some theories of grammatical categories.

I will have nothing to say about the categorial status of worth here; let it stand that no matter what category worth may belong to, it is an atypical example of the category.

Worth belongs to the categories of noun and adjective. The noun use (as in You should make an estimate of your net worth) is unproblematic and need not be considered further. As an adjective, however, worth is highly exceptional. Most importantly for present purposes, it licenses an NP complement, as in The paintings are [worth thousands of dollars]. In this respect, it is like a preposition, but overall the case for analyzing it as an adjective is strong.

Sometimes it is worth having a look at German where there is a noun der Wert and an adjective wert, one of those adjectives that can be connected with a number and a unit of measurement to indicate length, height and similar indications. Personally I don't think it good when in dictionaries the adjective worth is labelled as a preposition.
With a preposition you can't make sentences of the type

The analysis of worth as a preposition in its 'transitive' role seems most logical to me; it is generally unproblematic to replace 'to/at the value of' with 'for the purpose of' or 'in the direction of'. However 'to the value of' and 'red' share a lot less in common...